Since this is a geometric series, let's use the sum to n terms of a geometric series given by:
[tex]S_n = \frac{a(r^{n} - 1)}{r - 1}[/tex], where a is the first term, r is the common ratio, and n is the number of terms.
We know that a = 1
Common ratio (r): 2
Num. of terms: 10
Plugging it all into the equation, we produce:
[tex]S_{10} = \frac{1(2^{10} - 1)}{2 - 1}[/tex]
[tex] = 2^{10} - 1[/tex]
[tex]1,023[/tex]
Thus, the summation is 1,023
